zbMATH — the first resource for mathematics

Modifying the tropical version of Stickel’s key exchange protocol. (English) Zbl 07285954
Summary: A tropical version of Stickel’s key exchange protocol was suggested by D. Grigoriev and V. Shpilrain [Commun. Algebra 42, No. 6, 2624–2632 (2014; Zbl 1301.94114)] and successfully attacked by M. Kotov and A. Ushakov [J. Math. Cryptol. 12, No. 3, 137–141 (2018; Zbl 1397.94082)]. We suggest some modifications of this scheme that use commuting matrices in tropical algebra and discuss some possibilities of attacks on these new modifications. We suggest some simple heuristic attacks on one of our new protocols, and then we generalize the Kotov and Ushakov attack on tropical Stickel’s protocol and discuss the application of that generalized attack to all our new protocols.
15A80 Max-plus and related algebras
94A60 Cryptography
Full Text: DOI
[1] Butkovič, P., Max-Linear Systems: Theory and Algorithms, Springer Monographs in Mathematics. Springer, London (2010)
[2] Grigoriev, D.; Shpilrain, V., Tropical cryptography, Commun. Algebra 42 (2014), 2624-2632
[3] Grigoriev, D.; Shpilrain, V., Tropical cryptography II. Extensions by homomorphisms, Commun. Algebra 47 (2019), 4224-4229
[4] Jones, D., Special and Structured Matrices in Max-Plus Algebra: PhD Thesis, University of Birmingham, Birmingham (2018)
[5] Kotov, M.; Ushakov, A., Analysis of a key exchange protocol based on tropical matrix algebra, J. Math. Cryptol. 12 (2018), 137-141
[6] Linde, J.; Puente, M. J. de la, Matrices commuting with a given normal tropical matrix, Linear Algebra Appl. 482 (2015), 101-121
[7] Shpilrain, V., Cryptanalysis of Stickel’s key exchange scheme, Computer Science - Theory and Applications Lecture Notes in Computer Science 5010. Springer, Berlin (2008), 283-288
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.